In the figure, a 40.4 kg uniform square sign, of edge length L = 2.24 m, is hung

Question

In the figure, a 40.4 kg uniform square sign, of edge length L = 2.24 m, is hung from a horizontal rod of length d_h = 3.06 m and negligible mass. A cable is attached to the end of the rod and to a point on the wall at distance d_v = 4.87 m above the point where the rod is hinged to the wall. (a) What is the tension in the cable? (b) What is the horizontal component of the force on the rod from the wall? Take the positive direction to be to the right. (c) What is the vertical component of this force? Take the positive direction to be upward. (a) Number Units (b) Number Units (c) Number Units

Explanation / Answer

From the given data:
= arctan(4.87/3.06) = 57.85º

a) The weight of the sign acts at distance 2.24 m from the hinge.
Summing the moments about the hinge gives us
M = 0 = T*sin57.85 - 40.4 * 9.8* 2.24
T = 1047.48 N

b) The horizontal component pulls the rod toward the wall with force
F = Tcos = 1047.48* cos57.85 = 557.40 N

c) and therefore the wall must push (to the right) on the rod.

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